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The continuous uniform distribution is constant over the interval [a,b] and is zero elsewhere.
Returns the value at x of the density function of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The pdf $$ f(x; a, b) = \cases{ \displaystyle{1\over b-a} & for $0 \le x \le 1$ \cr \cr 0 & otherwise } $$
and is 0 otherwise.
Returns the value at x of the distribution function of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The cdf is $$ F(x; a, b) = \cases{ 0 & for $x < a$ \cr \cr \displaystyle{x-a\over b-a} & for $a \le x \le b$ \cr \cr 1 & for $x > b$ } $$
Returns the q-quantile of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b; in other words, this is the inverse of cdf_continuous_uniform. Argument q must be an element of [0,1]. To make use of this function, write first load("distrib").
Returns the mean of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The mean is $$ E[X] = {a+b\over 2} $$
Returns the variance of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The variance is $$ V[X] = {(b-a)^2\over 12} $$
Returns the standard deviation of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The standard deviation is $$ D[X] = {b-a \over 2\sqrt{3}} $$
Returns the skewness coefficient of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The skewness coefficient is $$ SK[X] = 0 $$
Returns the kurtosis coefficient of a
\({\it
ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first load("distrib").
The kurtosis coefficient is $$ KU[X] = -{6\over5} $$
Returns a
\({\it
ContinuousUniform}(a,b)\) random variate, with a<b. Calling random_continuous_uniform with a third argument n, a random sample of size n will be simulated.
This is a direct application of the random built-in Maxima function.
See also random. To make use of this function, write first load("distrib").
Next: Logistic Random Variable, Previous: Beta Random Variable, Up: Functions and Variables for continuous distributions [Contents][Index]